Premium
On the Laplace Transform of Radial Functions
Author(s) -
Trione Susana Elena
Publication year - 1991
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1991854303
Subject(s) - hankel transform , laplace transform , two sided laplace transform , mathematics , inverse laplace transform , laplace–stieltjes transform , mellin transform , mathematical analysis , laplace transform applied to differential equations , order (exchange) , derivative (finance) , post's inversion formula , function (biology) , green's function for the three variable laplace equation , pure mathematics , bessel function , fourier transform , fractional fourier transform , fourier analysis , finance , evolutionary biology , financial economics , economics , biology
Let ϕ ( t ) ( t ∈ R n be a radial function. Let f ( z ) be the Laplace transform of ϕ ( t ). Then a theorem due to A. Gonzá Domínguez shows that f ( z ) can be expressed as a Hankel transform. I prove two representation formulae which express the Laplace transform of radial functions by means of the m th‐order derivative of the Hankel transform of order 0 and − ½.